Work

Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation

Year: 2021

Type: article

Abstract: We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle (Y -∆) transformation at the critical point n = 2.We deduce the theorem of Matiyasevich and its inverse from the Biggs formula, and we apply this relation to construct the recursion on the parameter n.We provide two different proofs of the Zamolodchikov tetrahedron equation satisfied by the star-triangle transformation in the case of n = 2 multivariate Tutte polynomial, we extend the latter to the case of valency 2 points and show that the Biggs formula and the startriangle transformation commute.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2021.035

Authors: Boris Bychkov, Anton Kazakov, Dmitry Talalaev

Institutions: National Research University Higher School of Economics, Yaroslavl State University, Lomonosov Moscow State University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Russian Science Foundation

Award: G1787717288